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Removable singularities of Yang-Mills fields in \({\mathbb{R}}^ 3\). (English) Zbl 0552.58037
It is well known that the apparent point singularities in finite action solution of Yang-Mills fields in 4-dimensions may be removed by a gauge transformation. On the other hand, finite action does not seem to be the right condition in other dimensions. If \(n\geq 5\), the theorem is false as shown by examples which are in \(L^ p\) for \(2\leq p\leq n/2\), but not for \(p\geq n/2\). In 3-dimensions Jaffe and Taubes have shown the only finite action solution in all of space is identically zero. It was conjectured by Uhlenbeck that in dimension n, the relevant norm is the \(L^{n/2}\) norm, which is also the conformally invariant one. In the paper under review the author proves that apparent point singularities in solutions for which the \(L^{n/2}\) norm is finite \((n=3,5,6\) or 7) may be removed by a gauge transformation.
Reviewer: M.Puta

58J90 Applications of PDEs on manifolds
81T08 Constructive quantum field theory
Full Text: Numdam EuDML
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